Chapter 10 Switching DC Power Supplies • One of the most important applications of power electronics Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-1 Linear Power Supplies • Very poor efficiency and large weight and size Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-2 Switching DC Power Supply: Block Diagram • High efficiency and small weight and size Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-3 Switching DC Power Supply: Multiple Outputs • In most applications, several dc voltages are required, possibly electrically isolated from each other •High voltage translation ratios possible Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-4 Transformer Analysis • Needed to discuss high-frequency isolated supplies Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-5 PWM to Regulate Output • Basic principle is the same as discussed in Chapter 8 Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-6 Flyback Converter • Derived from buck-boost; very power at small power (> 50 W ) power levels Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-7 Flyback Converter • Switch on and off states (assuming incomplete core demagnetization) Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-8 Flyback Converter • Switching waveforms (assuming incomplete core demagnetization) Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-9 Other Flyback Converter Topologies • Not commonly used Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-10 Forward Converter • Derived from Buck; idealized to assume that the transformer is ideal (not possible in practice) Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-11 Forward Converter: in Practice • Switching waveforms (assuming incomplete core demagnetization) Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-12 Forward Converter: Other Possible Topologies • Two-switch Forward converter is very commonly used Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-13 Push-Pull Inverter • Leakage inductances become a problem Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-14 Half-Bridge Converter • Derived from Buck Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-15 Half‐bridge DC‐DC converter with transformer isolation • Primary windings current waveforms, • Also non‐centre‐tapped secondary windings current waveforms, • Concept of waveform duty ratio to represent ratio of total time switches conduct to the period Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-16 Evaluating RMS values • From the primary windings current waveform of a half‐ bridge DC‐DC converter with transformer isolation, the RMS value is obtained as: • , • , . . . • When secondary windings are non‐centre‐tapped, the expression for RMS current is similar to that for the primary windings current. Copyright © 2021 by Prof. MN Gitau. Chapter 10 Switching DC Power Supplies 10-17 Half‐bridge DC‐DC converter with transformer isolation • Centre‐tapped secondary windings current waveform, • Could also be high rectifier diodes current waveform Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-18 Evaluating RMS values • From centre‐tapped secondary windings current waveform, the RMS value is obtained as: . • . . , . • 0.5 0.5 , Copyright © 2021 by Prof. MN Gitau. Chapter 10 Switching DC Power Supplies 10-19 Half‐bridge DC‐DC converter with transformer isolation • Transformer windings voltage waveform, • Horizontal axis is normalised Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-20 Evaluating RMS values • From the primary windings voltage waveform, the RMS value is obtained as • , • , . . . • Following a similar approach, an expression for secondary windings RMS voltage is shown to be the same as that for the primary winding voltage. Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-21 Evaluating RMS values • From the output side circuit of a converter with a centre‐ tap, the following expression is obtained • , 0 • , • , Copyright © 2021 by Prof. MN Gitau , Chapter 10 Switching DC Power Supplies 10-22 Evaluating RMS values • From the output side circuit of a converter with no centre‐ tap, the following expression is obtained • • 0 2 , 2 , Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-23 Evaluating RMS values • , , , • , , , • , , , • Core size is proportional to the total apparent power processed by the various windings. • For a centre‐tapped winding, total apparent power is the sum of the contributions from each section of the winding, • When multiple windings are involved, the individual contributions are summed to obtain the total apparent power. Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-24 Evaluating RMS values • Again referring to the derivations for trapezoidal signals that were derived as part of EDF320. • From the primary windings current waveform, the top switch RMS value is obtained as: • . • • Device current rating are based on RMS current as it determines power dissipation. Copyright © 2021 by Prof. MN Gitau. Chapter 10 Switching DC Power Supplies 10-25 Full-Bridge Converter • Used at higher power levels (> 0.5 kW ) Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-26 Evaluating RMS values • From the primary windings current waveform of full‐ bridge DC‐DC converter with transformer isolation, the RMS value is obtained as: • , • , . . . • When secondary windings are non‐centre‐tapped, the expression for RMS current is similar to that for the primary windings current. Copyright © 2021 by Prof. MN Gitau. Chapter 10 Switching DC Power Supplies 10-27 Evaluating RMS values • From centre‐tapped secondary windings current waveform, the RMS value is obtained as: . • . . , . • 0.5 0.5 , Copyright © 2021 by Prof. MN Gitau. Chapter 10 Switching DC Power Supplies 10-28 Evaluating RMS values • From the primary windings voltage waveform, the RMS value is obtained as • , • , . . . • Following a similar approach, an expression for secondary windings RMS voltage is shown to be the same as that for the primary winding voltage. Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-29 Evaluating RMS values • From the output side circuit of a converter with a centre‐ tap, the following expression is obtained • , 0 • , • , Copyright © 2021 by Prof. MN Gitau 2 , Chapter 10 Switching DC Power Supplies 10-30 Evaluating RMS values • From the output side circuit of a converter with no centre‐ tap, the following expression is obtained • • 0 2 , 2 , Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-31 Evaluating RMS values • , , , • , , , • , , , • Core size is proportional to the total apparent power processed by the various windings. Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-32 Current-Source Converter • More rugged (no shoot‐through) but both switches must not be open simultaneously Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-33 Ferrite Core Material • Several materials to choose from based on applications Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-34 Core Utilization in Various Converter Topologies • At high switching frequencies, core losses limit excursion of flux density Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-35 Control to Regulate Voltage Output • Linearized representation of the feedback control system Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-36 Small‐signal modelling: buck converter • Small‐signal modelling entails the following steps: – Obtain first‐order differential equations to describe the dynamics of the energy storage components during each switching interval, – Average the first‐order differential equations using duty ratio as a weight, – Averaged equations describe the dynamics of the energy storage elements over a switching period, – Perturb the averaged equations and separate DC from AC terms, – Use the AC terms to obtain small‐signal transfer functions Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-37 Small‐signal modelling: buck converter • The first‐order equations describing the inductor and capacitor dynamics are obtained as follows, • For the interval when the self‐controlled switch is on: • , • , • • Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-38 Small‐signal modelling: buck converter • For the interval when the diode conducts: • 0 • • • Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-39 Small‐signal modelling: buck converter • Averaging the two sets of first‐order equations: • 1 , • • Perturb the averaged equations to yield • , 1 ̃ • Copyright © 2021 by Prof. MN Gitau ̃ Chapter 10 Switching DC Power Supplies 10-40 Small‐signal modelling: buck converter • Separate into DC and AC terms: • DC terms • 0 • , 1 , • 0 Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-41 Small‐signal modelling: buck converter • AC terms • ̃ • ̃ , ̃ • Laplace transform to yield • s ̃ , ̃ • Copyright © 2021 by Prof. MN Gitau ̃ Chapter 10 Switching DC Power Supplies 10-42 Small‐signal modelling: buck converter • Four different transfer functions can be obtained – – – – Relating inductor current dynamics to duty ratio variations, Relating inductor current dynamics to input voltage variations, Relating capacitor voltage dynamics to duty ratio variations, Relating capacitor voltage dynamics to input voltage variations, Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-43 Small‐signal modelling: buck converter • Transfer function relating inductor current dynamics to duty ratio variations, • Required when closing a current loop, • ̃ • ̃ , ̃ • Laplace transform to yield • s ̃ , ̃ • Copyright © 2021 by Prof. MN Gitau ̃ Chapter 10 Switching DC Power Supplies 10-44 Small‐signal modelling: buck converter • ̃ • Substitute into the equation for inductor current dynamics to eliminate capacitor voltage, • Rearrange to yield • 1 ̃ D , Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-45 Small‐signal modelling: buck converter • Transfer‐function relating inductor current to duty‐ratio variations is obtained as • ̃ , • Transfer‐function relating inductor current to input voltage variations is obtained as • ̃ Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-46 Small‐signal modelling: buck converter • ̃ • Substitute into the equation for inductor current dynamics to eliminate inductor current, • Rearrange to yield • 1 D , Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-47 Small‐signal modelling: buck converter • Transfer‐function relating capacitor voltage variations to duty‐ratio variations is obtained as • , • Transfer‐function relating capacitor voltage variations to input voltage variations is obtained as • • A similar approach can be adopted for any other type of DC‐DC converter including those with transformer isolation. Copyright © 2021 by Prof. MN Gitau Chapter 10 Switching DC Power Supplies 10-48 Forward Converter: An Example • The switch and the diode are assumed to be ideal Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-49 Forward Converter:Transfer Function Plots • Example considered earlier Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-50 Flyback Converter:Transfer Function Plots • An example Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-51 Linearizing the PWM Block • The transfer function is essentially a constant with zero phase shift Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-52 Gain of the PWM IC • It is slope of the characteristic Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-53 Typical Gain and Phase Plots of the OpenLoop Transfer Function • Definitions of the crossover frequency, phase and gain margins Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-54 A General Amplifier for Error Compensation • Can be implemented using a single op-amp Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-55 Type‐2 Error Amplifier • Shows phase boost at the crossover frequency Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-56 Voltage Feed-Forward • Makes converter immune from input voltage variations Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-57 Voltage versus Current Mode Control • Regulating the output voltage is the objective in both modes of control Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-58 Various Types of Current Mode Control • Constant frequency, peakcurrent mode control is used most frequently Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-59 Peak Current Mode Control • Slope compensation is needed Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-60 A Typical PWM Control IC • Many safety control functions are built in Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-61 Current Limiting • Two options are shown Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-62 Implementing Electrical Isolation in the Feedback Loop • Two ways are shown Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-63 Implementing Electrical Isolation in the Feedback Loop • A dedicated IC for this application is available Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-64 Input Filter • Needed to comply with the EMI and harmonic limits Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-65 ESR of the Output Capacitor • ESR often dictates the peak-peak voltage ripple Copyright © 2003 by John Wiley & Sons, Inc. Chapter 10 Switching DC Power Supplies 10-66
